*The following was first published in Scalefour News 194.*

Continuous Springy Beams (CSBs) have, over the last ten years or so, have proved themselves to be an elegant solution to the problem of providing a suspension system for finescale locos. However Foe many people there is a fundamental problem with them in that the placement of the anchor points that hold the spring wire is non-obvious. This has lead to the use of complicated spreadsheets determine these points, which is of putting to many people. I have long held the belief that what was needed was a simple rule of thumb method where the anchor point positions could be calculated with nothing more sophisticated than a calculator. Now after an afternoon of displacement activity, when I should have been working on something else, I have found the answer[1].

**Magic Numbers**

The problem that CSBs poses mathematically is that there are an infinite number of solutions. While we can discount many of these, for instance where the outer anchors lie outside the frames, there are still many other possible combinations of anchor that will give similar solutions. However there is one special case that gives a ‘magic number’ that will help with a more general solution.

If we use the case of a four coupled loco, it is obvious that if the centre anchor is placed midway between the axles and the outer anchors are arranged symmetrically the bottom of the curve that the spring takes up will occur at a point midway between the axles, i.e. at the central anchor point (Fig 1 A). Now if we move the outer anchor points, so that they stay symmetrical, there will be a point where the top points of the springs curve will be above each of the axles (Fig 1 B). From experience this point is about 0.3 of the wheelbase outside the axles. This relationship will remain true for all wheelbases that we are likely to use and it is also true however many axles there are. So 0.3 is are ‘magic number’ which we can use in future calculations.

**The Plot Thickens**

What I did was to take a symmetrical frame, in this case 8′ x 8′ (32 x 32mm), and built a plot using the spreadsheet to produce a range of wheelbases where the centre axle was progressively offset by 6” (2mm), while the outer anchor points were kept constant. This is shown in Fig 2. I occurred to me that, given I had not been too careful about choosing the ‘best’ outcome, that there were two relationships that were worth pursuing. One was that the lefthand inner anchor was a constant distance from the lefthand axle and that there was a relationship between the position of the righthand inner anchor and the offset of the centre axle. I went back to the spreadsheet and proved my conjectures by plugging in the calculated positions. After then testing the calculations on another wheelbase (6′ x 6′), I felt confident enough that the conjectures were correct to spent time finding all the edge cases to produce this:

This is a matrix of all the wheelbases where the rule of thumb gives an acceptable result. The *shorter* wheelbase is plotted on the vertically, while the *longer* wheelbase is plotted horizontally. A green block represents a wheelbase where the maximum and minimum weights on the axles are within about 2% of each other. The yellow blocks represent wheelbases which lie just outside the 2% limits or where they could be inside or outside the limit depending on how values are rounded. Looking at the matrix I think that most loco classes will well within the green part of the plot [2], but I would be glad to hear of any that are in the yellow blocks or even the uncoloured parts to the top right hand.

**The Rule of Thumb**

**Answers**

Does this mean that I don’t have to use the spreadsheet?

Not really, since the spreadsheet will give you information on the best size of spring wire to use and the position of the centre of gravity which will help to balance the loco. Also there may well be occasions where the calculated positions of the anchors coincide with some part of the structure of the frames, brake hangers in particular, then you will have to resort to the spreadsheet. You will, however, have a set of starting points for the anchors that will take ease finding a correct solution.

[1] Or maybe just one of many answers

[2] I have not counted any early French or Belgian locos in this.